Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Dynamics and Control of Trajectory Tubes

Theory and Computation

  • Book
  • © 2014

Overview

Authors:
  1. Alexander B. Kurzhanski

    1. Faculty of Computational Maths, Moscow State (Lomonosov) University, Moscow, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Pravin Varaiya

    1. Electrical Engineering, University of California, Berkeley, Berkeley, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Addresses significant control-theoretical problems, with emphasis on feedback control
  • Indicates the appropriate mathematical theory for these problems in terms of set-valued functions (trajectory tubes)
  • Discusses computational schemes that provide complete solutions to the problems and yield software tools that are applicable to systems of high dimension

Part of the book series: Systems & Control: Foundations & Applications (SCFA, volume 85)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 19.99 USD 39.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 29.99 USD 54.99
45% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 29.99 USD 54.99
45% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (11 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  2. Linear Control Systems

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 1-46

  3. The Dynamic Programming Approach

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 47-86

  4. Ellipsoidal Techniques: Reachability and Control Synthesis

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 87-145

  5. Solution Examples on Ellipsoidal Methods: Computation in High Dimensions

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 147-196

  6. The Comparison Principle: Nonlinearity and Nonconvexity

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 197-251

  7. Impulse Controls and Double Constraints

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 253-273

  8. Dynamics and Control Under State Constraints

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 275-309

  9. Trajectory Tubes State-Constrained Feedback Control

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 311-339

  10. Guaranteed State Estimation

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 341-370

  11. Uncertain Systems: Output Feedback Control

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 371-394

  12. Verification: Hybrid Systems

    • Alexander B. Kurzhanski, Pravin Varaiya
    Pages 395-429

  13. Back Matter

    Pages 431-445
    Download chapter PDF
Back to top

Keywords

About this book

This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

Authors and Affiliations

  • Faculty of Computational Maths, Moscow State (Lomonosov) University, Moscow, Russia

    Alexander B. Kurzhanski

  • Electrical Engineering, University of California, Berkeley, Berkeley, USA

    Pravin Varaiya

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation